题目描述

Byteasar works as a ticket inspector in a Byteotian National Railways (BNR) express train that connects Byteburg with Bitwise.

The third stage of the BNR reform (The never ending saga of BNR reforms and the Bitwise hub was presented in the problems Railway from the third stage of XIV Polish OI and Station from the third stage of XV Polish OI. Their knowledge, however, is not required at all in order to solve this problem.) has begun. In particular, the salaries system has already been changed.

For example, to encourage Byteasar and other ticket inspectors to efficient work, their salaries now depend on the number of tickets (passengers) they inspect. Byteasar is able to control all the passengers on the train in the time between two successive stations, but he is not eager to waste his energy in doing so. Eventually he decided he would check the tickets exactly $k$ times per ride.

Before setting out, Byteasar is given a detailed summary from which he knows exactly how many passengers will travel from each station to another. Based on that he would like to choose the moments of control in such a way that the number of passengers checked is maximal. Obviously, Byteasar is not paid extra for checking someone multiple times - that would be pointless, and would only disturb the passengers. Write a programme that will determine for Byteasar when he should check the tickets in order to maximise his revenue.

输入格式

In the first line of the standard input two positive integers $n$ and $k$ ($1 ≤ k < n ≤ 600$, $k ≤ 50$) are given. These are separated by a single space and denote, respectively, the number of stations en route and the number of controls Byteasar intends to make. The stations are numbered from $1$ to $n$ in the order of appearance on the route.

In the next $n-1$ lines the summary on passengers is given. The $(i+1)$-th line contains information on the passengers who enter the train on the station $i$ - it is a sequence of $n-i$ nonnegative integers $x_{i,i+1},x_{i,i+2},…,x_{i,n}$ separated by single spaces. The number $x_{i,j}$ (for $1 ≤ i < j ≤ n$) denotes the number of passengers who enter the train on station $i$ and leave it on station $j$. The total number of passengers (i.e. the sum of all $x_{i,j}$) does not exceed $2{,}000{,}000{,}000$.

输出格式

Your programme should print out (in a single line) an increasing sequence of $k$ integers from the interval from $1$ to $n-1$ separated by single spaces to the standard output. These numbers should be the numbers of stations upon leaving which Byteasar should control the tickets.

题目大意

有 $n$ 个车站，现在有一辆火车从 $1$ 到 $n$ 驶过，给出 $a_{i,j}$ 代表从 $i$ 站上车 $j$ 站下车的人的个数。列车行驶过程中你有 $K$ 次检票机会，所有当前在车上的人会被检票，问最多能检多少个不同的人的票。

输入格式

第一行正整数 $N,K$，$1≤K＜N≤600$，$K≤50$。接下来 $N-1$ 行，第 $i$ 行第 $j$ 个数描述第 $i$ 站上，到第 $i+j$ 站下的乘客个数。总乘客数 $≤2\times 10^9$。

输出格式

单调增的 $K$ 个整数，用空格隔开，表示经过哪些站以后查票。

7 2
2 1 8 2 1 0
3 5 1 0 1
3 1 2 2
3 5 6
3 2
1

2 5